The editor CP Scott famously said, in regard to his paper, The Manchester Guardian, "Opinions are free, but facts are sacred", and I think that is the key principle in any discussion that sets out to be fair.

Of course the complication is that opinions about what are the facts can differ - but in most cases it is possible to establish them objectively. A fair discussion of the different opinions people hold about what is the right thing to do can then proceed.

A commitment to fairness does not imply any duty to include those who refuse to accept facts which have been objectively proved beyond doubt. So much for flat-earthers and holocaust deniers.

But of course it is important not to stretch the category of "proved beyond doubt" to include things about which many, even most, are confident is true.
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The suggestion that "liberal" views are so established that other voices are silenced does not stand up to the briefest examination of the tabloid press in the UK. The BBC does have a legal obligation to be fair, which it sometimes seeks to meet in ways that are not wholly satisfactory, but the press has no such obligation, and in the case of most national newspapers, no desire to act in accordance with CP Scott's words which I quoted above.